The surface area of each triangular pyramid is approximately 35.85 cm².
From the problem description, we have the following information about the pyramid:
Base length (L): 3.9 cm
Base width (W): 4.5 cm
Height (H): 3.5 cm
We need to find the surface area, which includes the area of the base and the area of the lateral faces.
Calculate the Slant Height:
We can use the Pythagorean theorem to find it:
Slant Height^2 = Height^2 + (Base Width / 2)^2
Plugging in the values:
Slant Height^2 = 3.5 cm^2 + (4.5 cm / 2)^2 ≈ 15.5625 cm^2
Slant Height ≈ √15.5625 cm ≈ 4 cm (rounded to two decimal places)
The base of the pyramid is a triangle with a length of 3.9 cm and a width of 4.5 cm. Therefore, its area can be calculated using the formula:
Base Area = (Base Length * Base Width) / 2
Substituting the values:
Base Area = (3.9 cm * 4.5 cm) / 2 ≈ 8.85 cm²
Each of the three lateral faces of the pyramid is a triangle with the slant height as its hypotenuse and half the base width as its base. Therefore, the area of each lateral face can be calculated using the formula:
Lateral Face Area = (1/2) * Base Width * Slant Height
Since there are three lateral faces, the total lateral surface area is:
Total Lateral Surface Area = 3 * Lateral Face Area
Total Lateral Surface Area = 3 * (1/2) * 4.5 cm * 4 cm ≈ 27 cm²
Finally, add the base area and the total lateral surface area to find the total surface area of the pyramid:
Total Surface Area = Base Area + Total Lateral Surface Area
Total Surface Area = 8.85 cm² + 27 cm² ≈ 35.85 cm²
Therefore, the surface area of each triangular pyramid is approximately 35.85 cm².